The former Sheffield Wednesday midfielder was already familiar with Carvalhal.
Leeds United are reportedly in talks to re-sign the Swansea City defender.
Leeds are likely to be busy this summer after taking a step backwards in their hunt for promotion.
The former West Bromwich Albion midfielder previously advocated the appointment of his former captain Nigel Pearson.
The former Ipswich Town manager is the bookies favourite to take over at Leeds United - and a popular choice with some Whites fans.
The former Sheffield Wednesday midfielder says he's 'a big admirer' of Burnley's Dyche.
McCarthy left Ipswich Town on Tuesday, while Pearson - who was Palmer's captain at Sheffield Wednesday - is managing in Belgium.
Palmer played for both Leeds United and Sheffield Wednesday.
The former West Bromwich Albion midfielder was once captained by Pearson - the ex-Leicester City and Derby County boss.
Pontus Jansson is an important player for Leeds United.